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Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

This clear plastic semicircular protractor is divided by twenties and marked by two hundreds from 0 to 3,200 and from 3,200 to 6,400. A pinhole is at the origin point. The interior is labeled: ANGULAR MILS; 8016738. This protractor was item no. FAO-44. Felsenthal Instruments Company manufactured it for the U.S. Army about 1958.

The Felsenthal Instruments Company was the leading supplier of mathematical instruments to the U.S. Army Air Force and the U.S. Navy Bureau of Aeronautics, particularly during World War II (when the firm was known as G. Felsenthal & Sons). After the company ceased operations in approximately 1976, it provided a large sample of its products to the Smithsonian.

This clear plastic semicircular protractor is divided by ten mils and marked by hundreds from 100 to 3,100 in both the clockwise and counterclockwise directions. It is also divided by single degrees and marked by tens from 0° to 180° in both directions. Diagonal lines extend some of the measurement markings out to the edges of the rectangle surrounding the protractor. Pinholes are at the origin point and in the upper left and right corners. The interior of the protractor has cutout stencils for a circle, triangle, square, and two oblong shapes. The middle also contains scales placed at right angles to each other. They are divided and marked by hundreds from 1,000 to 2[00]. The scales are labeled: 1:21120.

The left edge of the rectangular plastic piece is divided by tenths of an inch and marked by ones from 1 to 3. Inside the 3-inch ruler is a scale for mils divided by hundreds and marked by thousands from 5,000 to 1,000. The scale continues on the top of the rectangle, again divided by hundreds and marked by thousands from 5,000 to 1,000. The scale is labeled: 1:62500. On the right side of the top is a scale labeled: 1:20,000. It is divided and marked by hundreds from 1,000 to 2[00]. This scale also repeats on the right side of the rectangle. On the right edge of the rectangle, there is a scale divided by millimeters and marked by ones from 1 to 7. It is labeled: METRIC.

The bottom of the protractor bears a scale divided by hundreds and marked by thousands from 1,000 to 8,000. It is labeled: 1:62500. The bottom edge has a second scale, divided by hundreds and marked by five hundreds from 500 to 3,000. It is labeled: 1:21120. The name of the instrument is printed on the very bottom edge: MAP COORDINATOR AND PROTRACTOR - A-10. Donor Ben Rau dated the object to 1942.

Maurice Hartung of the University of Chicago wrote this sixteen-page booklet to explain the use of natural log and logarithmic scales placed on Pickett's line of "dual-base" slide rules. Its citation information is: Maurice L. Hartung, How to Use Ln-L Scale Slide Rules (Santa Barbara, Calif.: Pickett, Inc., n.d.). The logo and address on the cover were in use from 1964.

Pickett used these scales on several models represented in the Smithsonian collections, including 3, 4, 515, 600, and 1010. The rules depicted in the booklet are models 1011 and 4, similar to 2000.0203.01. Hartung explains how to find logarithms and natural logs (by reading the mantissa), powers of e and 10, logarithms of proper fractions, powers for negative exponents, and the characteristic. He explains how to place the decimal point and how to correct for the error introduced when the number 2.3 is used to estimate e. He then covers multiplication, division, logarithms of combined operations, powers of other bases, hyperbolic functions, and applied problems.

This semicircular brass protractor is divided by single degrees and marked by tens from 0° to 180° in both the clockwise and counterclockwise directions. The bottom edge is indented so that a pencil or pricker may be placed at the origin point. The protractor bears three marks: POSTS; MADE IN GERMANY; and a fleur-de-lis pointing to the origin. The Frederick W. Post Company, a Chicago mathematical instruments dealer established in 1893, used the type style found on this protractor in the 1920s and 1930s. However, the brass protractor depicted in Post's 1936 catalog is not indented on its lower edge, and it shows an eagle under the maker's mark.

William J. Ellenberger (1908–2008) donated this object. He studied electrical and mechanical engineering at the George Washington University between 1925 and 1934. He then worked for the Potomac Electric Power Company and the National Bureau of Standards. During World War II, Ellenburger served in the U.S. Army Signal Corps. He was a civilian construction management engineer for the army from 1954 to 1968, when he became a private consultant.

In the early 1960s, the Chicago firm of Playskool introduced this educational toy for children three to six years old, seeking to give them an early familiarity with numbers. It has two rows of relatively large rotating wooden rectangular blocks, each with a row of square rotating wooden blocks below. The larger blocks have problems in simple addition written on them, the smaller ones answers. The problems and correct answers are written in the same color of paint. The blocks move on metal rods that are attached at top and bottom to a frame. The frame is supported at the back by a collapsible metal stand. The frame is painted with a pattern of bricks on the side and a roof at the top.

While many protractors simply measure angles in degrees, others have been adapted for more specialized contexts. For instance, they may be combined with other drawing instruments, such as rulers or templates for flow chart components. Or, they may make measurements in other scales for angles, such as radians. Before computerized and satellite navigation equipment was in wide use, protractors were employed in military applications, including positioning artillery.

Thus, this clear plastic protractor, which is in the shape of a sixth-circle, permitted the user to plot the distance traveled by a projectile from the time that elapsed before the sound of the projectile was heard. The outer edge of the protractor's arc is divided by hundredths and marked by tenths from +3.4 to +0.1 (in black print) and from -0.1 to -3.4 (in red print). The scale is labeled: TIME INTERVAL, SECONDS and MIDPOINTS FOR 4-SECOND SUB-BASE, 1/25000.

A scale marked DEGREES is further inside the arc. It is divided by minutes and marked by fives from 55° to 0°. Finally, a scale for MILS is divided by tens and marked by hundreds from 1000 to 100. 1000 mils is equivalent to 56.25°. A scale for THOUSANDS OF YARDS 1/25000 is along the right edge of the protractor. It is divided by five-hundredths and marked by ones from 14 to 1.

The Felsenthal Instruments Company was the leading supplier of mathematical instruments to the U.S. Army Air Force and the U.S. Navy Bureau of Aeronautics, particularly during World War II (when the firm was known as G. Felsenthal & Sons). After the company ceased operations in approximately 1976, it provided a large sample of its products to the Smithsonian.

This clear plastic sixth-circle protractor is divided along its outer edge by hundredths and marked by tenths from +1.7 to +0.1 (in black print) and from -0.1 to -3.4 (in red print). The scale is labeled: TIME INTERVAL, SECONDS. The left edge of the protractor is divided by tens and marked by hundreds from 2000 to 600. The scale is labeled: LENGTH OF SUB-BASE, YARDS. The right edge of the protractor is divided by halves and marked by ones from 14 to 1. The scale is labeled: THOUSANDS OF YARDS (/) 1/25000.

The interior of the protractor is filled with diagonal lines. Three scales are among the diagonal lines, each numbered by tenths in black and in red print. The outermost is numbered from 3.9 to 0.1; the middle scale is numbered from 3.0 to 0.1; and the innermost is numbered from 2.2 to 0.1.

The maker's mark is near the vertex, which is notched: 2 SOUND SECONDS (/) TEMPLATE, 1/25000 (/) FELSENTHAL INSTRUMENTS CO. (/) MFR'S PART NO. FAE-19B (/) MFR'S CODE 22040. There is a large plus sign to the right of the maker's mark.

The Chicago firm that manufactured this protractor was known as Felsenthal Instrument Co. in the 1960s and 1970s. Ben Wharton Rau (1904–1995) and his wife, Margery Felsenthal Rau (1916–2010), arranged the donation of this object and many other instruments to the Smithsonian. Margery's father, Irving (1887–1956), was one of the "Sons" of G. Felsenthal & Sons, as the company was known in the 1940s and 1950s. Margery's grandfather, Gabe Felsenthal, founded the firm in 1899.

Ben Rau worked for the Felsenthals. His duties included touring military facilities with a large display of the company's products. He catalogued hundreds of instruments when the company went out of business in 1976. He dated this protractor and 1977.1141.01 to 1950. While the form was indeed probably older, the maker's name on the instrument indicates it was manufactured in the 1960s or 1970s. Rau also held patents on a collapsible film reel, a proportional divider, and a belt buckle assembly.

This clear plastic sixth-circle protractor is graduated into 10 groups of 20 divisions, each labeled with the number 50. The unit of angular measure is mils, which was utilized in artillery applications. There are 6,400 mils in a circle (i.e., 1 mil = 0.05625 degrees). The arc on this instrument is 1,000 mils, or 56.25 degrees, in length.

An arm extends from the left side of the protractor. The arm is divided to half-units and marked by five (scaled) meters from 160 to 10. Two holes with diameters of 5mm are next to the 145–140 and 30–25 marks. The vertex of the protractor bears a small notch.

The interior of the protractor is marked: PROTRACTOR, RANGE DEFLECTION (/) SCALE 1:25,000 (/) RANGE 16,000 (/) METERS. Stamped inside a box is the text: THIS TRAINING AID WILL BE RETURNED (/) TO THE FIELD ARTILLERY SCHOOL (/) UPON COMPLETION OF THE SUB-COURSE (/) WITH WHICH ISSUED. Donor Ben Rau dated the instrument to 1965.

This clear plastic circular protractor is divided by tenths and marked by ones from 1 to 63. In the 48-64 quadrant, it is also marked in red print by ones from 32 to 17. The scale is labeled: AZIMUTH-MILS (100). The interior of the 16–32 quadrant is cut out. Each of the straight sides bears a scale divided by fifties and marked by thousands from 0 to 4,000. The scales are labeled: METERS RF 1: 50,000.

An arm extending from the 0-16 quadrant is divided by tenths and marked by ones from 1 to 17. The scale is labeled: RANGE METERS (1000). The interior of the 32–48 quadrant bears a maker's mark: FELSENTHAL INSTRUMENTS CO. (/) MFR'S CODE 22040 (/) MFR'S PART NO. FAE-28. The protractor was used to predict the direction and distance of artillery rounds. Donor Ben Rau wrote "Massengale" (which may refer to a particular U.S. Army officer) on the tag he provided with this instrument, and he dated the object to 1966.

This clear plastic rectangular protractor is divided by single degrees and marked by tens from 10° to 170° and from 190° to 350°. Pinholes near the 20° and 60° marks allow for positioning the protractor. The bottom edge is divided by tenths of an inch and marked by ones from 1" to 5". The interior of the protractor contains three scales of equal parts: 1) divided by hundreds and marked by five hundreds from 0 to 2,500 yards, for a scale of 1/20,000; 2) divided by hundreds and marked by thousands from 0 to 7,000 yards, for a scale of 1/62,500; and 3) divided by hundreds and marked by five hundreds from 0 to 2,000 meters, for a scale of 1/20,000. There are verniers to the left of the first and third scales.

Near the top of the protractor is marked: U.S. 1951. The 1951 is believed to refer to the date of the object. The maker's mark is: G. FELSENTHAL & SONS, INC. (/) PART NO. FAE-9.